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Hello Sir, I hope you are fine and fit. I have a question that I want to ask from you. What is difference between these two sentences? I has been waiting for them for 2 hours. And I was waiting for them for 20 minutes.

These sentences have different time references and a context is required to understand what those time references are.

The correct form of the first sentence is 'I have been waiting for them for 2 hours'. We use this when the waiting began in the past and continues up to the present - you are still waiting as you speak.

In the second sentence the waiting is all in the past; you are not waiting now and are telling someone about a past event. Generally we use 'was waiting' rather than 'waited' when the action was interrupted by another action. For example, we might say 'I was waiting for them for two hours before they arrived', where their arrival interrupts the waiting. However, without knowing the context of the sentence we can only guess at this.

So,as I have understood it,if I wanted to emphasize that she had not done her work by some moment in the past I would choose Past P.,and if I want to emphasize that her work still is not done(at present moment) then I choose Present P., and Past Simple (She told...) does't influence on my choice(Past P. or Present P.) ?

I wouldn't say the past simple doesn't influence the tense in the second clause, but it certainly doesn't determine it automatically. The two different forms express different meanings, i.e. refer to different times.

Hello again!
In one of your comments I saw such example:
'She told me that she has not done her work.'
I am a little bit confused,- shouldn't there be Past Perfect here instead of Present Perfect (She told me that she had not done her work) ,since as I see it the fact of her not having done her work refers to the past,i.e. to the time period limited by the moment when she told me this in the past? Or I am wrong in my assumptions?

Both the past perfect and the present perfect are possible here. If the action being described is still current then no tense shift is required. For example, take a look at these:

She said she loved me. [Perhaps she still loves me, perhaps she does not - we do not know]

She said she loves me. [She still loves me]

If you say 'has not done' then the situation is still current and has not been remedied - the work has still not been done. If you say 'had not done' then we understand that the situation is no longer current because the work has been completed in the meantime by someone.

Hello
I read this statement in Longman text book, in comprehension reading part, which is
"... and this time he did succeed."
Why the author said that "he did succeed" not "he succeeded" ?
Isn't "succeed' a verb ?

Without knowing the context I can't say for sure, but this looks to me like an instance of using 'did' for emphasis. This page explains how to use 'do' for emphasis -- 'did' can be used the same way when talking about the past.